A function n(x) satisfied the differential equation $\frac{{d}^{2}n\left(x\right)}{d{x}^{2}}-\frac{n\left(x\right)}{{L}^{2}}=0$ where L is a constant. The boundary conditions are: n(0)=K and n ( ∞ ) = 0. The solution to this equation is
The solution of the differential equation ${k}^{2}\frac{{d}^{2}y}{d{x}^{2}}=y-{y}_{2}$ under the boundary conditions (i) y = y_{1} at x = 0 and (ii) y = y_{2} at x = $\infty $, where k, y_{1 }and y_{2} are constants, is